Enthelpy as a state function

In summary: Paths_of_commuting_energyIn summary, Path A (reversible expansion at constant T) does zero work, while Path B (reversible expansion by releasing the gas to a vacuum to achieve V2 at adiabatic condition) does work.
  • #1
flamcsd
4
0
Consider gas here as idea gas.

The gas expands from state 1: P1, V1 and T1 to state 2: P2, V2, and T1 using two different paths:

Path A: reversible expansion at constant T
Path B: irreversible expansion by releasing the gas to a vacuum to achieve V2 at adiabatic condition.

Thing I confuse: consider that enthalpy as a state function: H1 to H2 from state 1 to state 2.

for reversible path A: dU = q + w. dU = 0. so q=-w. The system needs some q from surrounding to perform w. and dH = q. H2 = H1 + dH = H1 + q.

but for Path B: w=0, q=0, dU=0. dH=0. So, H2 = H1.

Why? my question is enthalpy can't be same for path B, because enthalpy is a state function which is independent from its path.
 
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  • #2
How did you arrive at w = 0 for the second expansion?

Don't forget that full expansion into a vacuum implies that P2 = 0 & V2 = ∞

The work done is pv work which is the area in the pv indicator diagram shown.

Between some point C at P3, V3 (say 1 atmosphere) and vacuum (unattainable) the work is shown by the hatched diagram.

If you take it all the way to infinity as shown the work is the area under the whole graph.

You need to integrate an equation of state for the gas to obtain this figure.
 

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  • #3
Thanks for your reply

the V2 in path B is assumed equal to V2 in path A. therefore, Path B and Path A could both reach a same state, P2, V2, and T1.

the vacuum part is V2-V1, it's like lift a barrier and let the gas go to extra V2-V1 part and reach V2. I don't want V2 go infinite.
 
  • #4
The point of state variables is that at any state there is one and only one value available to each state variable.

So to compare enthapies, start and end points have to be the same for both processes.
You started well by noting this.

At every point on each path there will be a well defined P and V.

You didn't answer the question about why you think w = 0 for the adiabatic irreversible path.

Path B and Path A could both reach a same state, P2, V2, and T1.

You are trying to specify P, V and T. You only specifiy two of these the third is not independent it is determined by the other two already specified
 
  • #5
Hi Studiot,

Thanks for the discussion. To answer your quesion:

"why you think w = 0 for the adiabatic irreversible path"

my path B is a free expansion path. a free expansion path does zero work.
see Free_expansion in wikipedia.

And actually, I only try to specify two variables P and V, where T is kept constant as T1. sorry for not clear.
 
  • #6
Wiki also says

.......which implies that one cannot define thermodynamic parameters as values of the gas as a whole. For example, the pressure changes locally from point to point, and the volume occupied by the gas (which is formed of particles) is not a well defined quantity.
 
  • #7
Studiot said:
Wiki also says

yes, I am not picking any state variable in the middle of the free expansion. what i want to do is comparing the state function H enthalpy at the start and the end of the free expansion.

apparently, the enthalpy change for a free expansion is zero.

However, by taking another reversible Path A at constant T. the enthalpy change is not zero.

The thing is the start state (P1, V1, T1), end state (P2, V2, T1) of Path A and B are exactly the same. I want to expect the same enthalpy change for path A and B.

however, this is not the case. This confuses me a lot if we take enthalpy as a state function, who is independent of the paths.
 
  • #8

1. What is enthalpy?

Enthalpy is a thermodynamic state function that represents the total energy of a system, including both its internal energy and the work required to change its volume at a constant pressure.

2. How is enthalpy different from internal energy?

Internal energy only accounts for the energy within a system, while enthalpy also considers the energy required to change the system's volume at a constant pressure.

3. Why is enthalpy considered a state function?

Enthalpy is considered a state function because its value only depends on the current state of the system, not on how the system reached that state. This means that the enthalpy of a system is the same regardless of the pathway taken to reach that state.

4. How is enthalpy measured in a system?

Enthalpy is measured in joules (J) or kilojoules (kJ), which are units of energy. It can be measured experimentally using calorimetry, which involves measuring the heat exchange between a system and its surroundings.

5. What are some real-life applications of enthalpy?

Enthalpy is used in a variety of industries, such as in power plants to calculate the efficiency of energy production, in chemistry to predict the outcomes of reactions, and in HVAC systems to regulate temperature and humidity in buildings. It is also used in the design and analysis of engines, turbines, and other machines.

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